Magnesium-24 energy level diagram

Energy levels and transitions of neutral ²⁴Mg (Mg I, nuclear spin I = 0): 18 levels and 61 lines below 2 µm, each with its vacuum wavelength, frequency and, for 23 of them, the reduced dipole matrix element. Level energies come from the NIST Atomic Spectra Database; transition rates are 61 NIST. Neutral magnesium is also the starting point for loading Mg⁺ ion traps by photoionisation.

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Download: diagram (PDF) diagram (SVG) transitions (CSV) levels (CSV) source code

Key transitions of ²⁴Mg

λ, ν from NIST level energies unless a measured frequency for this isotope is available. A: measured value or NIST. Γ/2π: natural linewidth of the upper level, 1/(2πτ).

Isotope shifts

Shift = ν(first isotope) − ν(second isotope).

Closed and nearly closed transitions of ²⁴Mg

A transition is closed when its upper level can decay only to the level it was excited from, so the atom keeps scattering photons. “closed”: among the levels NIST lists, no other level below the upper level has the opposite parity and |ΔJ| ≤ 1, so no other electric-dipole decay exists. Otherwise the leak is the sum of the branching ratios of the other decay lines of the upper level (or 1 − branching ratio where that of the line itself has been measured), and the number of photons is 1 / leak. “≥” and “≤”: at least one possible decay path has no listed rate, so the leak is a lower limit. These numbers are derived from the branching ratios, lifetimes and rates of this page, not measured as such; the tag names the weakest of the inputs, * marks theory and ≈ a model or semi-empirical calculation. Listed: lines that start on the ground level or on a metastable level and leak at most 10 %, unless more than three possible decay paths have no listed rate. Fine-structure levels only: hyperfine and Zeeman dark states and forbidden decays without a listed rate are not considered. Select a line in the diagram for the full list of its leak channels.

All ²⁴Mg transitions below 2 µm

Reduced dipole matrix elements follow the convention A = ω³|d|²/(3πε₀ħc³(2J′+1)), with J′ the upper level. Tags show where a number comes from: measured, NIST compilation, high-accuracy theory, a semi-empirical calculation (Kurucz line list, used only where no measurement or NIST value exists; typically within a factor 2), or a model calculation.

²⁴Mg energy levels

Mg⁺ ionisation limit 61671.05 cm⁻¹ = 7.64624 eV (162.151 nm)

Sources

• Aldenius, Tanner, Johansson, Lundberg, Ryan, Astron. Astrophys. 461, 767 (2007) [arXiv:as…
• Friebe et al., 'Remote frequency measurement of the 1S0-3P1 transition in laser cooled 24…
• Hannemann, Salumbides, Witte, Zinkstok, van Duijn, Eikema, Ubachs, Phys. Rev. A 74, 01250…
• Hansen, Therkildsen, Malossi, Jensen, van Ooijen, Brusch, Muller, Hald, Thomsen, Phys. Re…
• Jensen, He, Westergaard, Gunnarsson, Madsen, Brusch, Hald, Thomsen, Phys. Rev. Lett. 107,…
• Jonsson, Kroll, Persson, Svanberg, Phys. Rev. A 30, 2429 (1984); quoted in Table 1 of Peh…
• Kulosa et al., Phys. Rev. Lett. 115, 240801 (2015) [arXiv:1508.01118]: 655 058 646 691(10…
• Kwiatkowski, Teppner, Zimmermann, Z. Phys. A 294, 109 (1980), laser excitation; quoted in…
• Larsson & Svanberg, Z. Phys. D 25, 127 (1993), pulsed level-crossing (Hanle) spectroscopy…
• Lurio, Phys. Rev. 136, A376 (1964), zero-field level crossing (Hanle) on an atomic beam (…
• NIST ASD
• NIST ASD level energies
• Porsev & Derevianko, Phys. Rev. A 69, 042506 (2004) [arXiv:physics/0312006], Table IV: hy…
• Salumbides, Hannemann, Eikema, Ubachs, MNRAS 373, L41 (2006), frequency-comb calibrated p…

Isotope shifts are nu(first) - nu(second) in MHz. On 1S0-3P1, 1S0-3P0, 1S0-1P1 and 3P-3D the heavier isotope lies at HIGHER frequency (positive 26-24); on the 517 nm 3P-4s 3S1 triplet the heavier isotope lies at LOWER frequency (negative 26-24): He et al. print unsigned 'Delta 24-26' values and the sign was fixed from Hallstadius & Hansen as quoted by Berengut et al. 2005 / Aldenius et al. 2007. Frequencies refer to 24Mg unless an 'isotope' key says otherwise; NIST level energies in this file are natural-mixture values copied from data/nist/Mg_I_levels.tsv. frequency_THz values given with wavenumber_cm were converted with c = 299792458 m/s. Entries with method 'compilation' were read in a later paper/thesis that quotes the original experiment (original named in 'source'). Fields marked 'derived here' are simple differences/centroids/1-over-rate of quoted numbers. Non-schema keys used: alternatives, note, natural_linewidth_MHz, magic_wavelength_nm, quadratic_zeeman_MHz_per_T2, lattice_light_shift_slope, hyperfine_components_25Mg_MHz, wavenumber_cm, intercombination_decay_rate_s, unc_plus/unc_minus, nuclear_moment_muN. 3P1 lifetime: experiments (4.0-5.3 ms) sit above most theory (2.8-3.8 ms). 4s 3S1 lifetime: experiments scatter 9.7-14.8 ns. 3P2 lifetime 2050 s is for 24Mg; 25Mg is shortened by hyperfine quenching (theory). Photoionization: Mg is ionized by resonance-enhanced two-photon ionization at 285 nm: 3s2 1S0 -> 3s3p 1P1 (35051.264 cm^-1) followed by a second 285 nm phot

Atoms with measured data

• Lithium-632 levels, 85 lines
• Lithium-732 levels, 85 lines
• Beryllium-917 levels, 26 lines
• Sodium-2336 levels, 106 lines
• Magnesium-2518 levels, 61 lines
• Potassium-3934 levels, 84 lines
• Potassium-4034 levels, 84 lines
• Potassium-4134 levels, 84 lines
• Calcium-4035 levels, 61 lines
• Calcium-4335 levels, 61 lines
• Chromium-5256 levels, 87 lines
• Chromium-5356 levels, 87 lines
• Rubidium-8536 levels, 94 lines
• Rubidium-8736 levels, 94 lines
• Strontium-8440 levels, 70 lines
• Strontium-8640 levels, 70 lines
• Strontium-8740 levels, 70 lines
• Strontium-8840 levels, 70 lines
• Cadmium-11115 levels, 21 lines
• Cadmium-11315 levels, 21 lines
• Cadmium-11415 levels, 21 lines
• Caesium-13331 levels, 79 lines
• Barium-13744 levels, 89 lines
• Barium-13844 levels, 89 lines
• Dysprosium-16139 levels, 55 lines
• Dysprosium-16239 levels, 55 lines
• Dysprosium-16339 levels, 55 lines
• Dysprosium-16439 levels, 55 lines
• Erbium-16673 levels, 90 lines
• Erbium-16773 levels, 90 lines
• Erbium-16873 levels, 90 lines
• Thulium-16972 levels, 73 lines
• Ytterbium-17118 levels, 26 lines
• Ytterbium-17318 levels, 26 lines
• Ytterbium-17418 levels, 26 lines
• Mercury-19927 levels, 47 lines
• Mercury-20127 levels, 47 lines
• Mercury-20227 levels, 47 lines

All elements: periodic table